{"id":1668,"date":"2021-08-26T19:51:11","date_gmt":"2021-08-26T19:51:11","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/?post_type=chapter&#038;p=1668"},"modified":"2022-02-01T19:54:16","modified_gmt":"2022-02-01T19:54:16","slug":"solving-multi-step-equations","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/solving-multi-step-equations\/","title":{"raw":"Solving Multi-Step Equations","rendered":"Solving Multi-Step Equations"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\n<ul>\r\n \t<li>Solve multi-step equations<\/li>\r\n<\/ul>\r\n<\/div>\r\nWe solve equations using properties of real numbers and <strong>properties of equality<\/strong>.\r\n<div class=\"textbox shaded\">\r\n<h3>Properties of Equality<\/h3>\r\nFor two expressions [latex]S[\/latex] and [latex]T[\/latex] and any constant [latex]c[\/latex]:\r\n\r\n<strong>Addition Property of Equality:<\/strong> If [latex] S=T[\/latex] then [latex]S+c=T+c[\/latex]\r\n\r\n<strong>Multiplication Property of Equality:<\/strong> If [latex]S=T[\/latex] then [latex]S \\cdot c = T \\cdot c[\/latex], provided [latex]c \\neq 0[\/latex]\r\n\r\n<\/div>\r\nThese properties tell us we can add an expression to both sides of an equation and multiply each side of an equation by a nonzero expression to obtain an equivalent equation.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nSolve each equation:\r\n<ol>\r\n \t<li>[latex]x+1=7[\/latex]<\/li>\r\n \t<li>[latex]3x=45[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"228129\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"228129\"]\r\n\r\n<strong>a.<\/strong>\u00a0To solve an equation our goal is to isolate the variable. That is, get an equivalent equation of the form variable [latex]=[\/latex] number. In the equation [latex]x+1=7[\/latex] we need to have the variable <em>x<\/em> alone on one side of the equation. To remove the constant term [latex]1[\/latex] on the left side, we use the additive property of equality to add the additive inverse of [latex]1[\/latex] to each side of the equation.\r\n<p style=\"text-align: center;\">[latex]x+1=7[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]x+1+(-1)=7+(-1)[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]x+0=6[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]x=6[\/latex]<\/p>\r\nSince adding [latex]-1[\/latex] is the same as subtracting [latex]1[\/latex], we often say we subtract [latex]1[\/latex] from each side of the equation. We can check our solution in the original equation.\r\n<p style=\"text-align: center;\">[latex]6+1=7[\/latex]<\/p>\r\n<strong>b.<\/strong>\u00a0To solve the equation [latex]3x=45[\/latex] we need to remove the constant factor [latex]3[\/latex] from the left side. We do this by multiplying each side by its multiplicative inverse (reciprocal), [latex]\\frac{1}{3}[\/latex].\r\n<p style=\"text-align: center;\">[latex]3x=45[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{1}{3} \\cdot 3x = \\frac{1}{3} \\cdot 45[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]1 \\cdot x = \\frac{45}{3}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]x=15[\/latex]<\/p>\r\nSince multiplying by [latex]\\frac{1}{3}[\/latex] produces the same result as dividing by [latex]3[\/latex], we often say we divide each side of the equation by [latex]3[\/latex]. We can check our solution in the original equation.\r\n<p style=\"text-align: center;\">[latex]3 \\cdot 15 = 45[\/latex]<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox shaded\">\r\n<h3>Solving Multi-step Equations<\/h3>\r\n<ol>\r\n \t<li>(Optional) Multiply to clear any fractions or decimals.<\/li>\r\n \t<li>Simplify each side by clearing parentheses and combining like terms.<\/li>\r\n \t<li>Add or subtract to isolate the variable term\u2014possibly a term with the variable.<\/li>\r\n \t<li>Multiply or divide to isolate the variable.<\/li>\r\n \t<li>Check the solution.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nSolve for [latex]a[\/latex].\r\n\r\n[latex]4\\left(2a+3\\right)=28[\/latex]\r\n\r\n[reveal-answer q=\"372387\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"372387\"]\r\n\r\nApply the distributive property to expand [latex]4\\left(2a+3\\right)[\/latex] to [latex]8a+12[\/latex].\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}4\\left(2a+3\\right)=28\\\\ 8a+12=28\\end{array}[\/latex]<\/p>\r\nSubtract [latex]12[\/latex]\u00a0from both sides to isolate\u00a0the variable term.\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}8a+12\\,\\,\\,=\\,\\,\\,28\\\\ \\underline{-12\\,\\,\\,\\,\\,\\,-12}\\\\ 8a\\,\\,\\,=\\,\\,\\,16\\end{array}[\/latex]<\/p>\r\nDivide both terms by [latex]8[\/latex] to get a coefficient of [latex]1[\/latex].\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}\\underline{8a}=\\underline{16}\\\\8\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,8\\\\a\\,=\\,\\,2\\end{array}[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\n[latex]a=2[\/latex][\/hidden-answer]\r\n\r\n<\/div>\r\nIn the video that follows, we show another example of how to use the distributive property to solve a multi-step linear equation.\r\n\r\nhttps:\/\/youtu.be\/aQOkD8L57V0\r\n\r\nIn the next example we have parenthesis on each side of the equation, so we need to apply the distributive property on each side.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nSolve for [latex]t[\/latex].\r\n\r\n[latex]2\\left(4t-5\\right)=-3\\left(2t+1\\right)[\/latex]\r\n\r\n[reveal-answer q=\"302387\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"302387\"]\r\n\r\nApply the distributive property to expand [latex]2\\left(4t-5\\right)[\/latex] to [latex]8t-10[\/latex] and [latex]-3\\left(2t+1\\right)[\/latex] to[latex]-6t-3[\/latex]. Be careful in this step\u2014you are distributing a negative number, so keep track of the sign of each number after you multiply.\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}2\\left(4t-5\\right)=-3\\left(2t+1\\right)\\,\\,\\,\\,\\,\\, \\\\ 8t-10=-6t-3\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\end{array}[\/latex]<\/p>\r\nAdd [latex]-6t[\/latex] to both sides to begin combining like terms.\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}8t-10=-6t-3\\\\ \\underline{+6t\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,+6t}\\,\\,\\,\\,\\,\\,\\,\\\\ 14t-10=\\,\\,\\,\\,-3\\,\\,\\,\\,\\,\\,\\,\\end{array}[\/latex]<\/p>\r\nAdd [latex]10[\/latex] to both sides of the equation to isolate <em>t<\/em>.\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}14t-10=-3\\\\ \\underline{+10\\,\\,\\,+10}\\\\ 14t=\\,\\,\\,7\\,\\end{array}[\/latex]<\/p>\r\nThe last step is to divide both sides by [latex]14[\/latex] to completely isolate <em>t<\/em>.\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}14t=7\\,\\,\\,\\,\\\\\\frac{14t}{14}=\\frac{7}{14}\\end{array}[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\n[latex]t=\\frac{1}{2}[\/latex]\r\n\r\nWe simplified the fraction [latex]\\frac{7}{14}[\/latex] into [latex]\\frac{1}{2}[\/latex].[\/hidden-answer]\r\n\r\n<\/div>\r\nIn the following video, we solve another multi-step equation with two sets of parentheses.\r\n\r\nhttps:\/\/youtu.be\/StomYTb7Xb8\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question]2493-20478[\/ohm_question]\r\n\r\n<\/div>\r\nIf an equation contains fractions, it is sometimes helpful to clear fractions by multiplying both sides of the equation by the lowest common denominator of all fractions in the equation.\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nSolve \u00a0[latex]\\frac{1}{2}x-3=2-\\frac{3}{4}x[\/latex] by clearing the fractions in the equation first.\r\n\r\n[reveal-answer q=\"129951\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"129951\"]\r\n\r\nMultiply both sides of the equation by [latex]4[\/latex], the common denominator of the fractional coefficients.\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}\\frac{1}{2}x-3=2-\\frac{3}{4}x\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\\\\\\\ 4\\left(\\frac{1}{2}x-3\\right)=4\\left(2-\\frac{3}{4}x\\right)\\end{array}[\/latex]<\/p>\r\nUse the distributive property to expand the expressions on both sides.\u00a0Multiply.\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}4\\left(\\frac{1}{2}x\\right)-4\\left(3\\right)=4\\left(2\\right)-4\\left(\\frac{3}{4}x\\right)\\\\\\\\ \\frac{4}{2}x-12=8-\\frac{12}{4}x\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\, \\\\\\\\ 2x-12=8-3x\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\, \\end{array}[\/latex]<\/p>\r\nAdd [latex]3x[\/latex] to both sides to move the variable terms to only one side. Add [latex]12[\/latex] to both sides to move the variable\u00a0terms to only one side.\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}2x-12=8-3x\\, \\\\\\underline{+3x\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,+3x}\\\\ 5x-12=8\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\end{array}[\/latex]<\/p>\r\nAdd [latex]12[\/latex] to both sides to move the <b>constant<\/b> terms to the other side.\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}5x-12=8\\,\\,\\\\ \\underline{\\,\\,\\,\\,\\,\\,+12\\,+12} \\\\5x=20\\end{array}[\/latex]<\/p>\r\nDivide to isolate the variable.\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}\\underline{5x}=\\underline{5}\\\\ 5\\,\\,\\,\\,\\,\\,\\,\\,\\,5\\\\ x=4\\end{array}[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\n[latex]x=4[\/latex][\/hidden-answer]\r\n\r\n<\/div>\r\nIn the following video, we show how to solve a multi-step equation with fractions.\r\n\r\nhttps:\/\/youtu.be\/AvJTPeACTY0\r\n\r\n&nbsp;","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<ul>\n<li>Solve multi-step equations<\/li>\n<\/ul>\n<\/div>\n<p>We solve equations using properties of real numbers and <strong>properties of equality<\/strong>.<\/p>\n<div class=\"textbox shaded\">\n<h3>Properties of Equality<\/h3>\n<p>For two expressions [latex]S[\/latex] and [latex]T[\/latex] and any constant [latex]c[\/latex]:<\/p>\n<p><strong>Addition Property of Equality:<\/strong> If [latex]S=T[\/latex] then [latex]S+c=T+c[\/latex]<\/p>\n<p><strong>Multiplication Property of Equality:<\/strong> If [latex]S=T[\/latex] then [latex]S \\cdot c = T \\cdot c[\/latex], provided [latex]c \\neq 0[\/latex]<\/p>\n<\/div>\n<p>These properties tell us we can add an expression to both sides of an equation and multiply each side of an equation by a nonzero expression to obtain an equivalent equation.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Solve each equation:<\/p>\n<ol>\n<li>[latex]x+1=7[\/latex]<\/li>\n<li>[latex]3x=45[\/latex]<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q228129\">Show Answer<\/span><\/p>\n<div id=\"q228129\" class=\"hidden-answer\" style=\"display: none\">\n<p><strong>a.<\/strong>\u00a0To solve an equation our goal is to isolate the variable. That is, get an equivalent equation of the form variable [latex]=[\/latex] number. In the equation [latex]x+1=7[\/latex] we need to have the variable <em>x<\/em> alone on one side of the equation. To remove the constant term [latex]1[\/latex] on the left side, we use the additive property of equality to add the additive inverse of [latex]1[\/latex] to each side of the equation.<\/p>\n<p style=\"text-align: center;\">[latex]x+1=7[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]x+1+(-1)=7+(-1)[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]x+0=6[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]x=6[\/latex]<\/p>\n<p>Since adding [latex]-1[\/latex] is the same as subtracting [latex]1[\/latex], we often say we subtract [latex]1[\/latex] from each side of the equation. We can check our solution in the original equation.<\/p>\n<p style=\"text-align: center;\">[latex]6+1=7[\/latex]<\/p>\n<p><strong>b.<\/strong>\u00a0To solve the equation [latex]3x=45[\/latex] we need to remove the constant factor [latex]3[\/latex] from the left side. We do this by multiplying each side by its multiplicative inverse (reciprocal), [latex]\\frac{1}{3}[\/latex].<\/p>\n<p style=\"text-align: center;\">[latex]3x=45[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{1}{3} \\cdot 3x = \\frac{1}{3} \\cdot 45[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]1 \\cdot x = \\frac{45}{3}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]x=15[\/latex]<\/p>\n<p>Since multiplying by [latex]\\frac{1}{3}[\/latex] produces the same result as dividing by [latex]3[\/latex], we often say we divide each side of the equation by [latex]3[\/latex]. We can check our solution in the original equation.<\/p>\n<p style=\"text-align: center;\">[latex]3 \\cdot 15 = 45[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox shaded\">\n<h3>Solving Multi-step Equations<\/h3>\n<ol>\n<li>(Optional) Multiply to clear any fractions or decimals.<\/li>\n<li>Simplify each side by clearing parentheses and combining like terms.<\/li>\n<li>Add or subtract to isolate the variable term\u2014possibly a term with the variable.<\/li>\n<li>Multiply or divide to isolate the variable.<\/li>\n<li>Check the solution.<\/li>\n<\/ol>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Solve for [latex]a[\/latex].<\/p>\n<p>[latex]4\\left(2a+3\\right)=28[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q372387\">Show Solution<\/span><\/p>\n<div id=\"q372387\" class=\"hidden-answer\" style=\"display: none\">\n<p>Apply the distributive property to expand [latex]4\\left(2a+3\\right)[\/latex] to [latex]8a+12[\/latex].<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}4\\left(2a+3\\right)=28\\\\ 8a+12=28\\end{array}[\/latex]<\/p>\n<p>Subtract [latex]12[\/latex]\u00a0from both sides to isolate\u00a0the variable term.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}8a+12\\,\\,\\,=\\,\\,\\,28\\\\ \\underline{-12\\,\\,\\,\\,\\,\\,-12}\\\\ 8a\\,\\,\\,=\\,\\,\\,16\\end{array}[\/latex]<\/p>\n<p>Divide both terms by [latex]8[\/latex] to get a coefficient of [latex]1[\/latex].<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}\\underline{8a}=\\underline{16}\\\\8\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,8\\\\a\\,=\\,\\,2\\end{array}[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>[latex]a=2[\/latex]<\/p><\/div>\n<\/div>\n<\/div>\n<p>In the video that follows, we show another example of how to use the distributive property to solve a multi-step linear equation.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Solving an Equation with One Set of Parentheses\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/aQOkD8L57V0?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>In the next example we have parenthesis on each side of the equation, so we need to apply the distributive property on each side.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Solve for [latex]t[\/latex].<\/p>\n<p>[latex]2\\left(4t-5\\right)=-3\\left(2t+1\\right)[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q302387\">Show Solution<\/span><\/p>\n<div id=\"q302387\" class=\"hidden-answer\" style=\"display: none\">\n<p>Apply the distributive property to expand [latex]2\\left(4t-5\\right)[\/latex] to [latex]8t-10[\/latex] and [latex]-3\\left(2t+1\\right)[\/latex] to[latex]-6t-3[\/latex]. Be careful in this step\u2014you are distributing a negative number, so keep track of the sign of each number after you multiply.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}2\\left(4t-5\\right)=-3\\left(2t+1\\right)\\,\\,\\,\\,\\,\\, \\\\ 8t-10=-6t-3\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\end{array}[\/latex]<\/p>\n<p>Add [latex]-6t[\/latex] to both sides to begin combining like terms.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}8t-10=-6t-3\\\\ \\underline{+6t\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,+6t}\\,\\,\\,\\,\\,\\,\\,\\\\ 14t-10=\\,\\,\\,\\,-3\\,\\,\\,\\,\\,\\,\\,\\end{array}[\/latex]<\/p>\n<p>Add [latex]10[\/latex] to both sides of the equation to isolate <em>t<\/em>.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}14t-10=-3\\\\ \\underline{+10\\,\\,\\,+10}\\\\ 14t=\\,\\,\\,7\\,\\end{array}[\/latex]<\/p>\n<p>The last step is to divide both sides by [latex]14[\/latex] to completely isolate <em>t<\/em>.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}14t=7\\,\\,\\,\\,\\\\\\frac{14t}{14}=\\frac{7}{14}\\end{array}[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>[latex]t=\\frac{1}{2}[\/latex]<\/p>\n<p>We simplified the fraction [latex]\\frac{7}{14}[\/latex] into [latex]\\frac{1}{2}[\/latex].<\/p><\/div>\n<\/div>\n<\/div>\n<p>In the following video, we solve another multi-step equation with two sets of parentheses.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Solving an Equation with Parentheses on Both Sides\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/StomYTb7Xb8?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm2493\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=2493-20478&theme=oea&iframe_resize_id=ohm2493&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>If an equation contains fractions, it is sometimes helpful to clear fractions by multiplying both sides of the equation by the lowest common denominator of all fractions in the equation.<\/p>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Solve \u00a0[latex]\\frac{1}{2}x-3=2-\\frac{3}{4}x[\/latex] by clearing the fractions in the equation first.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q129951\">Show Solution<\/span><\/p>\n<div id=\"q129951\" class=\"hidden-answer\" style=\"display: none\">\n<p>Multiply both sides of the equation by [latex]4[\/latex], the common denominator of the fractional coefficients.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}\\frac{1}{2}x-3=2-\\frac{3}{4}x\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\\\\\\\ 4\\left(\\frac{1}{2}x-3\\right)=4\\left(2-\\frac{3}{4}x\\right)\\end{array}[\/latex]<\/p>\n<p>Use the distributive property to expand the expressions on both sides.\u00a0Multiply.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}4\\left(\\frac{1}{2}x\\right)-4\\left(3\\right)=4\\left(2\\right)-4\\left(\\frac{3}{4}x\\right)\\\\\\\\ \\frac{4}{2}x-12=8-\\frac{12}{4}x\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\, \\\\\\\\ 2x-12=8-3x\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\, \\end{array}[\/latex]<\/p>\n<p>Add [latex]3x[\/latex] to both sides to move the variable terms to only one side. Add [latex]12[\/latex] to both sides to move the variable\u00a0terms to only one side.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}2x-12=8-3x\\, \\\\\\underline{+3x\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,+3x}\\\\ 5x-12=8\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\end{array}[\/latex]<\/p>\n<p>Add [latex]12[\/latex] to both sides to move the <b>constant<\/b> terms to the other side.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}5x-12=8\\,\\,\\\\ \\underline{\\,\\,\\,\\,\\,\\,+12\\,+12} \\\\5x=20\\end{array}[\/latex]<\/p>\n<p>Divide to isolate the variable.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}\\underline{5x}=\\underline{5}\\\\ 5\\,\\,\\,\\,\\,\\,\\,\\,\\,5\\\\ x=4\\end{array}[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>[latex]x=4[\/latex]<\/p><\/div>\n<\/div>\n<\/div>\n<p>In the following video, we show how to solve a multi-step equation with fractions.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-3\" title=\"Solving an Equation with Fractions (Clear Fractions)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/AvJTPeACTY0?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>&nbsp;<\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-1668\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Revision and Adaptation. <strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Solving an Equation with One Set of Parentheses. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/aQOkD8L57V0\">https:\/\/youtu.be\/aQOkD8L57V0<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Solving an Equation with Parentheses on Both Sides. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/StomYTb7Xb8\">https:\/\/youtu.be\/StomYTb7Xb8<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Solving an Equation with Fractions (Clear Fractions). <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/AvJTPeACTY0\">https:\/\/youtu.be\/AvJTPeACTY0<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Unit 10: Solving Equations and Inequalities, from Developmental Math: An Open Program. <strong>Provided by<\/strong>: Monterey Institute of Technology and Education. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/nrocnetwork.org\/resources\/downloads\/nroc-math-open-textbook-units-1-12-pdf-and-word-formats\/\">http:\/\/nrocnetwork.org\/resources\/downloads\/nroc-math-open-textbook-units-1-12-pdf-and-word-formats\/<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Question ID: 2493, 20478. <strong>Authored by<\/strong>: Lippman, D; Martin, J. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: IMathAS Community License CC-BY + GPL<\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>College Algebra: Using Properties of Real Numbers. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":169134,"menu_order":4,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"Revision and Adaptation\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Unit 10: Solving Equations and Inequalities, from Developmental Math: An Open Program\",\"author\":\"\",\"organization\":\"Monterey Institute of Technology and Education\",\"url\":\"http:\/\/nrocnetwork.org\/resources\/downloads\/nroc-math-open-textbook-units-1-12-pdf-and-word-formats\/\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Solving an Equation with One Set of Parentheses\",\"author\":\"James Sousa (Mathispower4u.com) for Lumen Learning\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/aQOkD8L57V0\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Solving an Equation with Parentheses on Both Sides\",\"author\":\"James Sousa (Mathispower4u.com) for Lumen Learning\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/StomYTb7Xb8\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Solving an Equation with Fractions (Clear Fractions)\",\"author\":\"James Sousa (Mathispower4u.com) for Lumen Learning\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/AvJTPeACTY0\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc-attribution\",\"description\":\"College Algebra: Using Properties of Real Numbers\",\"author\":\"\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Question ID: 2493, 20478\",\"author\":\"Lippman, D; 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